This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 02db0f525a288673aba4923c6b88677071850d51.
Case data is captured from the NICD National COVID-19 Daily Report [3]. This contains the daily cases reported by the NICD for South Africa by province. Data is shown by specimen reported date. Most recent data is excluded due to incomplete reporting of tests in last number of days.
The following fixes are applied:
The methodology is described in detail here.
Below a 7-day moving average daily case count is plotted by province on a log scale since start of the epidemic:
Below the above chart is repeated for the last 30-days:
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| province | Count (Week) | Week Ending | Reproduction Number [95% Confidence Interval] |
|---|---|---|---|
| Eastern Cape | 119 | 2021-03-24 | 0.9 [0.76 - 1.08] |
| Free State | 772 | 2021-03-24 | 1.0 [0.95 - 1.10] |
| Gauteng | 1,942 | 2021-03-24 | 0.9 [0.90 - 0.99] |
| KwaZulu-Natal | 679 | 2021-03-24 | 0.7 [0.64 - 0.76] |
| Limpopo | 178 | 2021-03-24 | 0.9 [0.78 - 1.06] |
| Mpumalanga | 784 | 2021-03-24 | 0.9 [0.84 - 0.97] |
| North West | 637 | 2021-03-24 | 0.9 [0.86 - 1.01] |
| Northern Cape | 615 | 2021-03-24 | 0.9 [0.83 - 0.98] |
| Western Cape | 935 | 2021-03-24 | 1.0 [0.94 - 1.07] |
| South Africa | 6,661 | 2021-03-24 | 0.9 [0.89 - 0.94] |
Estimated Effective Reproduction Number by Province
Below estimates of the reproductive number is plotted on maps of South Africa [4].
Estimated Effective Reproduction Number Based on Cases by Province
Below the results for South Africa ove the last 90 days is plotted.
Estimated Effective Reproduction Number Based on Cases for South Africa over Time
Below the reproduction number by week by province is animated:
The results for each province over last 90 days is plotted below.
Estimated Effective Reproduction Number Based on Cases for Eastern Cape over Time
Estimated Effective Reproduction Number Based on Cases for Free State over Time
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
Estimated Effective Reproduction Number Based on Cases for KwaZulu-Natal over Time
Estimated Effective Reproduction Number Based on Cases for Limpopo over Time
Estimated Effective Reproduction Number Based on Cases for Mpumalanga over Time
Estimated Effective Reproduction Number Based on Cases for Northern Cape over Time
Estimated Effective Reproduction Number Based on Cases for Gauteng over Time
Estimated Effective Reproduction Number Based on Cases for Western Cape over Time
Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]
Further to the above the estimates are made under assumption that the cases are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers.
Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred earlier. These figures have not been shifted back.
Despite these limitation it is believed that the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
Having said all the above it would appear that the effective reproduction number was reasonably high in South Africa from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133.
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013.
[3] National Institute for Communicable Diseases, “National COVID-19 Daily Report,” 2021.
[4] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018.